The Federal Government has signalled it may be prepared to back the establishment of a national anti-corruption commission, but has slammed a model put forward by the bolstered Lower House crossbench as too heavy handed.

Key points:

Cathy McGowan's bill comes after a Senate motion calling on Parliament to formally support an anti-corruption commission

Ms McGowan hopes to hear back from Government within a week

Attorney-General Christian Porter said cautious consideration needed to find the right model, will take time and effort

Independent MP Cathy McGowan introduced her bill to the House on Monday morning, claiming the Coalition could no longer oppose an integrity commission.

Labor, the Greens and minor parties have long campaigned for a corruption watchdog, arguing current systems are woefully inadequate.

It is the first day the Morrison Government has had to navigate Parliament without a majority, following the swearing in of new Independent MP for Wentworth Kerryn Phelps.

The Government has previously dismissed the need for new integrity measures but Mr Morrison told Question Time that work had been underway for months.

"We are not opposed to measures which add and lift the integrity of the way Government is administered in this country and so we do not remain closed to those options," he said.

"We'll be considering a range of options about what is the best way to go forward."

Ms McGowan's bill follows a motion from the Senate earlier in the month, calling on Parliament to formally support an anti-corruption commission.

The Lower House did not formally discuss Ms McGowan's bill, but some used debate on the Senate motion to assess the merits for an anti-corruption commission.

Attorney-General Christian Porter said the matter needed "sober and cautious consideration" before an appropriate model could be put forward.

"The question about how any government or any parliament might improve the integrity framework at a federal level is a live question and one that should be under constant review and there are very potential paths forward that can mean for real improvement in that area," Mr Porter told the House.

In a wide-ranging critique, Mr Porter argued even journalists could be found guilty of corruption under the model proposed by Ms McGowan.

He cited a ruling by the communications watchdog, ACMA, that the ABC's political editor Andrew Probyn had failed to be impartial in his description of former prime minister Tony Abbott.

"Under this bill before the House, no ifs, ands, or buts, Andrew Probyn would be found to have committed corruption," he claimed.

"Any ABC journalist or SBS journalist, as a public servant and public official, who criticised the government in a way that … breached a code of conduct, that was perhaps found to have committed contempt or defamation and attracted a civil penalty, under this bill ... [would be subject to] a finding of corrupt conduct."

Ms McGowan responded saying she was prepared to work with the Coalition to find an agreeable proposal.

"From the bottom of my heart I hope the government will come back and tell us this week," she said.

"Most of your backbench seems to be in favour of it."

Speculation had been growing earlier in the day that Nationals MP Llew O'Brien would cross the floor and vote with Labor, the Greens and crossbench to support the Senate motion.

But a formal vote did not eventuate, with the both sides of the chamber agreeing to it without voting.

It remains unclear if, or when, the Parliament will consider Ms McGowan's bill.

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